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<div class="title">Poisson2DFiniteDifference.py</div>  </div>
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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00010"></a>00010 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00011"></a>00011 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00014"></a>00014 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00015"></a>00015 <span class="comment">#</span>
<a name="l00016"></a>00016 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00017"></a>00017 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00018"></a>00018 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00019"></a>00019 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00020"></a>00020 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00021"></a>00021 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00022"></a>00022 <span class="comment"># SOFTWARE.</span>
<a name="l00023"></a>00023 <span class="comment">#</span>
<a name="l00024"></a>00024 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00025"></a>00025 <span class="comment"># Mountain View, CA</span>
<a name="l00026"></a>00026 
<a name="l00027"></a>00027 <span class="stringliteral">&quot;&quot;&quot; solve poisson equation in 2D and direchlet bc. &quot;&quot;&quot;</span>
<a name="l00028"></a>00028 
<a name="l00029"></a>00029 <span class="keyword">from</span> numpy <span class="keyword">import</span> floor, linspace, meshgrid, roll, tile
<a name="l00030"></a>00030 <span class="keyword">from</span> numpy <span class="keyword">import</span> c_, asarray, ones, empty
<a name="l00031"></a>00031 
<a name="l00032"></a>00032 <span class="keyword">from</span> scipy.sparse.construct <span class="keyword">import</span> spdiags
<a name="l00033"></a>00033 <span class="keyword">from</span> scipy.sparse.linalg <span class="keyword">import</span> spsolve <span class="keyword">as</span> spsolve
<a name="l00034"></a>00034 
<a name="l00035"></a>00035 <span class="keyword">from</span> itertools <span class="keyword">import</span> izip, count
<a name="l00036"></a>00036 
<a name="l00037"></a>00037 
<a name="l00038"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html">00038</a> <span class="keyword">class </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html">Poisson2DFiniteDifference</a>(object):
<a name="l00039"></a>00039 
<a name="l00040"></a>00040     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00041"></a>00041 <span class="stringliteral">      Solve Poisson equation in 2D using a five points stencil, FD scheme.</span>
<a name="l00042"></a>00042 <span class="stringliteral">      We assume Dirichlet boundary conditions on the grid.</span>
<a name="l00043"></a>00043 <span class="stringliteral">      Only Dirichlet because that&#39;s what we need for calibrating</span>
<a name="l00044"></a>00044 <span class="stringliteral">      Volatility.</span>
<a name="l00045"></a>00045 <span class="stringliteral"></span>
<a name="l00046"></a>00046 <span class="stringliteral">      Carl Charrella, Mark Craddock and Nadima El-Hassan. The Calibration of stock option</span>
<a name="l00047"></a>00047 <span class="stringliteral">      pricing models using inverse problem methodology</span>
<a name="l00048"></a>00048 <span class="stringliteral"></span>
<a name="l00049"></a>00049 <span class="stringliteral">      Solve the problem</span>
<a name="l00050"></a>00050 <span class="stringliteral"></span>
<a name="l00051"></a>00051 <span class="stringliteral">            -div( grad ( u(x,y) ) ) = f</span>
<a name="l00052"></a>00052 <span class="stringliteral">            Dirichlet Boundary conditions.</span>
<a name="l00053"></a>00053 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00054"></a>00054     __slots__ = [
<a name="l00055"></a>00055         <span class="stringliteral">&#39;m_dx&#39;</span>,
<a name="l00056"></a>00056         <span class="stringliteral">&#39;m_dy&#39;</span>,
<a name="l00057"></a>00057         <span class="stringliteral">&#39;m_xmin&#39;</span>,
<a name="l00058"></a>00058         <span class="stringliteral">&#39;m_xmax&#39;</span>,
<a name="l00059"></a>00059         <span class="stringliteral">&#39;m_ymin&#39;</span>,
<a name="l00060"></a>00060         <span class="stringliteral">&#39;m_ymax&#39;</span>,
<a name="l00061"></a>00061         <span class="stringliteral">&#39;m_nx_pts&#39;</span>,
<a name="l00062"></a>00062         <span class="stringliteral">&#39;m_ny_pts&#39;</span>,
<a name="l00063"></a>00063         <span class="stringliteral">&#39;m_xgrid&#39;</span>,
<a name="l00064"></a>00064         <span class="stringliteral">&#39;m_ygrid&#39;</span>,
<a name="l00065"></a>00065         <span class="stringliteral">&#39;m_xgposi&#39;</span>,
<a name="l00066"></a>00066         <span class="stringliteral">&#39;m_ygposi&#39;</span>,
<a name="l00067"></a>00067         <span class="stringliteral">&#39;m_left&#39;</span>,
<a name="l00068"></a>00068         <span class="stringliteral">&#39;m_right&#39;</span>,
<a name="l00069"></a>00069         <span class="stringliteral">&#39;m_bott&#39;</span>,
<a name="l00070"></a>00070         <span class="stringliteral">&#39;m_top&#39;</span>,
<a name="l00071"></a>00071         <span class="stringliteral">&#39;m_eng_ready&#39;</span>,
<a name="l00072"></a>00072         <span class="stringliteral">&#39;m_ltype&#39;</span>,
<a name="l00073"></a>00073         <span class="stringliteral">&#39;m_load_len&#39;</span>,
<a name="l00074"></a>00074         <span class="stringliteral">&#39;m_vright&#39;</span>,
<a name="l00075"></a>00075         <span class="stringliteral">&#39;m_vtop&#39;</span>,
<a name="l00076"></a>00076         <span class="stringliteral">&#39;m_vbott&#39;</span>,
<a name="l00077"></a>00077         <span class="stringliteral">&#39;m_vleft&#39;</span>,
<a name="l00078"></a>00078         <span class="stringliteral">&#39;m_load&#39;</span>,
<a name="l00079"></a>00079         ]
<a name="l00080"></a>00080 
<a name="l00081"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac585dea79f7256fefec51c716bce4ec1">00081</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac585dea79f7256fefec51c716bce4ec1">__init__</a>(self):
<a name="l00082"></a>00082         <span class="stringliteral">&quot;&quot;&quot; instantiate object of type Poisson2D. &quot;&quot;&quot;</span>
<a name="l00083"></a>00083 
<a name="l00084"></a>00084         (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aeab92cfb5555af93f50f30ec33483881">m_dx</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a017d63e67d5db1c3fe99db3e76d7c89a">m_dy</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00085"></a>00085         (self.m_xmin, self.m_xmax) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00086"></a>00086         (self.m_ymin, self.m_ymax) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00087"></a>00087 
<a name="l00088"></a>00088         (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00089"></a>00089         (self.m_xgposi, self.m_ygposi) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00090"></a>00090         (self.m_nx_pts, self.m_ny_pts) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00091"></a>00091 
<a name="l00092"></a>00092         (self.m_bott, self.m_top) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00093"></a>00093         (self.m_left, self.m_right) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00094"></a>00094         (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a013aa4245d515d33f955facb8d86d53f">m_eng_ready</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aab73d1b44efb032b62ccf3ba1dd066b1">m_ltype</a>) = (<span class="keyword">False</span>, <span class="stringliteral">&#39;continuos&#39;</span>)
<a name="l00095"></a>00095         (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a06aa951c5a8718334ceec867d234aaaf">m_load_len</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a9b86acf66c46bfa5519828984fff2cd2">m_vright</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00096"></a>00096         (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aad8f636d52615cd0fe663c7d5a8c8fc1">m_vtop</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a13a04da3595fe00cd04c52009a098d17">m_vbott</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00097"></a>00097         (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a2c48b2c09079e26101bb882e86250edd">m_vleft</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac2a8f1bd5e621a18ad891dd886803902">m_load</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00098"></a>00098 
<a name="l00099"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a85ccb046fff0dc6fb7387306f6887d02">00099</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a85ccb046fff0dc6fb7387306f6887d02">set_xlxr</a>(self, left, right):
<a name="l00100"></a>00100         <span class="stringliteral">&quot;&quot;&quot; set left and right bc &quot;&quot;&quot;</span>
<a name="l00101"></a>00101 
<a name="l00102"></a>00102         (self.m_left, self.m_right) = (left, right)
<a name="l00103"></a>00103 
<a name="l00104"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a6213e6fe184b260e108ceece27b1d74c">00104</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a6213e6fe184b260e108ceece27b1d74c">set_bott_top</a>(self, bott, top):
<a name="l00105"></a>00105         <span class="stringliteral">&quot;&quot;&quot; set bottom and top bc &quot;&quot;&quot;</span>
<a name="l00106"></a>00106 
<a name="l00107"></a>00107         (self.m_bott, self.m_top) = (bott, top)
<a name="l00108"></a>00108 
<a name="l00109"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a07b2bed580699c913df804984760778d">00109</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a07b2bed580699c913df804984760778d">set_dx_dy</a>(self, delta_x, delta_y):
<a name="l00110"></a>00110         <span class="stringliteral">&quot;&quot;&quot; set grid delta x delta y &quot;&quot;&quot;</span>
<a name="l00111"></a>00111 
<a name="l00112"></a>00112         (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aeab92cfb5555af93f50f30ec33483881">m_dx</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a017d63e67d5db1c3fe99db3e76d7c89a">m_dy</a>) = (delta_x, delta_y)
<a name="l00113"></a>00113 
<a name="l00114"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ab271288fc08199e656dbd41ecfb736f6">00114</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ab271288fc08199e656dbd41ecfb736f6">set_continuos_load</a>(self, continuos_load):
<a name="l00115"></a>00115         <span class="stringliteral">&quot;&quot;&quot; make load a function. &quot;&quot;&quot;</span>
<a name="l00116"></a>00116 
<a name="l00117"></a>00117         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aab73d1b44efb032b62ccf3ba1dd066b1">m_ltype</a> = <span class="stringliteral">&#39;continuos&#39;</span>
<a name="l00118"></a>00118         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac2a8f1bd5e621a18ad891dd886803902">m_load</a> = continuos_load
<a name="l00119"></a>00119 
<a name="l00120"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a165b420a3eee93ce1e366cce8e7a47f7">00120</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a165b420a3eee93ce1e366cce8e7a47f7">set_discrete_load</a>(self, discrete_load):
<a name="l00121"></a>00121         <span class="stringliteral">&quot;&quot;&quot; make load a matrix. Two different interfaces are used for</span>
<a name="l00122"></a>00122 <span class="stringliteral">            clarity.</span>
<a name="l00123"></a>00123 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00124"></a>00124 
<a name="l00125"></a>00125         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aab73d1b44efb032b62ccf3ba1dd066b1">m_ltype</a> = <span class="stringliteral">&#39;discrete&#39;</span>
<a name="l00126"></a>00126         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac2a8f1bd5e621a18ad891dd886803902">m_load</a> = discrete_load
<a name="l00127"></a>00127 
<a name="l00128"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a63b57a290daf7f7f06550054aaeb8bb1">00128</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a63b57a290daf7f7f06550054aaeb8bb1">get_load</a>(self):
<a name="l00129"></a>00129         <span class="stringliteral">&quot;&quot;&quot; get load &quot;&quot;&quot;</span>
<a name="l00130"></a>00130 
<a name="l00131"></a>00131         load = self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a0293665f1db42b303ddebb00896aabba">__get_load</a>()
<a name="l00132"></a>00132         <span class="keywordflow">return</span> (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>[1, -1], self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>[-1, 1], load)
<a name="l00133"></a>00133 
<a name="l00134"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a5ed8a680bbc70e476a1a17ba6ae4632a">00134</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a5ed8a680bbc70e476a1a17ba6ae4632a">set_simu_domain</a>(self, leftx, botty, rightx, topy):
<a name="l00135"></a>00135         <span class="stringliteral">&quot;&quot;&quot; set boundary conditions &quot;&quot;&quot;</span>
<a name="l00136"></a>00136 
<a name="l00137"></a>00137         (self.m_xmin, self.m_xmax) = (float(leftx), float(rightx))
<a name="l00138"></a>00138         (self.m_ymin, self.m_ymax) = (float(botty), float(topy))
<a name="l00139"></a>00139 
<a name="l00140"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a6093f1f049af7d7604a30b82482430d6">00140</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a6093f1f049af7d7604a30b82482430d6">reset_engine</a>(self):
<a name="l00141"></a>00141         <span class="stringliteral">&quot;&quot;&quot; reset pde solver &quot;&quot;&quot;</span>
<a name="l00142"></a>00142 
<a name="l00143"></a>00143         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a013aa4245d515d33f955facb8d86d53f">m_eng_ready</a> = <span class="keyword">False</span>
<a name="l00144"></a>00144 
<a name="l00145"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a562f4485376749d89cb465f7ae2a69b9">00145</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a562f4485376749d89cb465f7ae2a69b9">get_mesh</a>(self):
<a name="l00146"></a>00146         <span class="stringliteral">&quot;&quot;&quot; 2D grid use to solve the pde. &quot;&quot;&quot;</span>
<a name="l00147"></a>00147 
<a name="l00148"></a>00148         <span class="keywordflow">if</span> self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a> <span class="keywordflow">is</span> <span class="keywordtype">None</span> <span class="keywordflow">or</span> self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a> <span class="keywordflow">is</span> <span class="keywordtype">None</span>:
<a name="l00149"></a>00149             self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a032131b3687e8715b976800f754a88a0">set_up_engine</a>()
<a name="l00150"></a>00150         <span class="keywordflow">return</span> (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>)
<a name="l00151"></a>00151 
<a name="l00152"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac25ae4cc5647612813893dcfd98df398">00152</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac25ae4cc5647612813893dcfd98df398">get_indx_grid</a>(self):
<a name="l00153"></a>00153         <span class="stringliteral">&quot;&quot;&quot; grid to values dicrete load &quot;&quot;&quot;</span>
<a name="l00154"></a>00154 
<a name="l00155"></a>00155         <span class="keywordflow">if</span> self.m_xgposi <span class="keywordflow">is</span> <span class="keywordtype">None</span> <span class="keywordflow">or</span> self.m_ygposi <span class="keywordflow">is</span> <span class="keywordtype">None</span>:
<a name="l00156"></a>00156             self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a032131b3687e8715b976800f754a88a0">set_up_engine</a>()
<a name="l00157"></a>00157 
<a name="l00158"></a>00158         <span class="keywordflow">return</span> (self.m_xgposi, self.m_ygposi)
<a name="l00159"></a>00159 
<a name="l00160"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a032131b3687e8715b976800f754a88a0">00160</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a032131b3687e8715b976800f754a88a0">set_up_engine</a>(self):
<a name="l00161"></a>00161         <span class="stringliteral">&quot;&quot;&quot; get ready for solving the pde. &quot;&quot;&quot;</span>
<a name="l00162"></a>00162 
<a name="l00163"></a>00163         <span class="keywordflow">if</span> self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a013aa4245d515d33f955facb8d86d53f">m_eng_ready</a>:
<a name="l00164"></a>00164             <span class="keywordflow">return</span>
<a name="l00165"></a>00165 
<a name="l00166"></a>00166         <span class="keyword">assert</span> self.m_xmax &gt; self.m_xmin
<a name="l00167"></a>00167         <span class="keyword">assert</span> self.m_ymax &gt; self.m_ymin
<a name="l00168"></a>00168         <span class="keyword">assert</span> 0 &lt; self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aeab92cfb5555af93f50f30ec33483881">m_dx</a> <span class="keywordflow">and</span> 0 &lt; self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a017d63e67d5db1c3fe99db3e76d7c89a">m_dy</a>
<a name="l00169"></a>00169 
<a name="l00170"></a>00170         nxsegs = int(floor((self.m_xmax - self.m_xmin) / self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aeab92cfb5555af93f50f30ec33483881">m_dx</a>))
<a name="l00171"></a>00171         nysegs = int(floor((self.m_ymax - self.m_ymin) / self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a017d63e67d5db1c3fe99db3e76d7c89a">m_dy</a>))
<a name="l00172"></a>00172         (self.m_nx_pts, self.m_ny_pts) = (max(nxsegs + 1, 3),
<a name="l00173"></a>00173                 max(nysegs + 1, 3))
<a name="l00174"></a>00174 
<a name="l00175"></a>00175         <span class="comment"># adjust dx, dy</span>
<a name="l00176"></a>00176         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aeab92cfb5555af93f50f30ec33483881">m_dx</a> = (self.m_xmax - self.m_xmin) / nxsegs
<a name="l00177"></a>00177         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a017d63e67d5db1c3fe99db3e76d7c89a">m_dy</a> = (self.m_ymax - self.m_ymin) / nysegs
<a name="l00178"></a>00178 
<a name="l00179"></a>00179         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a06aa951c5a8718334ceec867d234aaaf">m_load_len</a> = self.m_nx_pts * self.m_ny_pts - 2 \
<a name="l00180"></a>00180             * (self.m_nx_pts + self.m_ny_pts - 2)
<a name="l00181"></a>00181 
<a name="l00182"></a>00182         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a> = asarray(linspace(self.m_xmin, self.m_xmax,
<a name="l00183"></a>00183                                 self.m_nx_pts, <span class="stringliteral">&#39;True&#39;</span>))
<a name="l00184"></a>00184         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a> = asarray(linspace(self.m_ymin, self.m_ymax,
<a name="l00185"></a>00185                                 self.m_ny_pts, <span class="stringliteral">&#39;True&#39;</span>))
<a name="l00186"></a>00186 
<a name="l00187"></a>00187         (self.m_xgposi, self.m_ygposi) = (range(self.m_nx_pts),
<a name="l00188"></a>00188                 range(self.m_ny_pts))
<a name="l00189"></a>00189 
<a name="l00190"></a>00190         <span class="comment"># Boundary conditions</span>
<a name="l00191"></a>00191 
<a name="l00192"></a>00192         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a13a04da3595fe00cd04c52009a098d17">m_vbott</a> = self.m_bott(c_[self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>,
<a name="l00193"></a>00193                                    ones(self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>.shape)
<a name="l00194"></a>00194                                    * self.m_ymin])
<a name="l00195"></a>00195         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aad8f636d52615cd0fe663c7d5a8c8fc1">m_vtop</a> = self.m_top(c_[self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>,
<a name="l00196"></a>00196                                  ones(self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>.shape)
<a name="l00197"></a>00197                                  * self.m_ymax])
<a name="l00198"></a>00198         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a2c48b2c09079e26101bb882e86250edd">m_vleft</a> = self.m_left(c_[ones(self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>.shape)
<a name="l00199"></a>00199                                    * self.m_xmin, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>])
<a name="l00200"></a>00200         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a9b86acf66c46bfa5519828984fff2cd2">m_vright</a> = self.m_right(c_[ones(self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>.shape)
<a name="l00201"></a>00201                 * self.m_xmax, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>])
<a name="l00202"></a>00202 
<a name="l00203"></a>00203         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a013aa4245d515d33f955facb8d86d53f">m_eng_ready</a> = <span class="keyword">True</span>
<a name="l00204"></a>00204 
<a name="l00205"></a>00205     <span class="keyword">def </span>_eval_continuos_load(self, values):
<a name="l00206"></a>00206         <span class="stringliteral">&quot;&quot;&quot; compute load using analytical formula &quot;&quot;&quot;</span>
<a name="l00207"></a>00207 
<a name="l00208"></a>00208         <span class="keywordflow">return</span> self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac2a8f1bd5e621a18ad891dd886803902">m_load</a>(values)
<a name="l00209"></a>00209 
<a name="l00210"></a>00210     <span class="keyword">def </span>_eval_discrete_load(self, coor):
<a name="l00211"></a>00211         <span class="stringliteral">&quot;&quot;&quot; values load represented as a matrix &quot;&quot;&quot;</span>
<a name="l00212"></a>00212 
<a name="l00213"></a>00213         <span class="keywordflow">return</span> self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ac2a8f1bd5e621a18ad891dd886803902">m_load</a>[coor[0], coor[1]]
<a name="l00214"></a>00214 
<a name="l00215"></a>00215     <span class="keyword">def </span>__get_load(self):
<a name="l00216"></a>00216         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00217"></a>00217 <span class="stringliteral">            We are using lexicographic order to assemble the matrix.</span>
<a name="l00218"></a>00218 <span class="stringliteral">            starting from the bottom left all the way up right.</span>
<a name="l00219"></a>00219 <span class="stringliteral">            Assumes that the Image is lower-left</span>
<a name="l00220"></a>00220 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00221"></a>00221 
<a name="l00222"></a>00222         load = empty((self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a06aa951c5a8718334ceec867d234aaaf">m_load_len</a>, 1), <span class="stringliteral">&#39;float&#39;</span>)
<a name="l00223"></a>00223 
<a name="l00224"></a>00224         <span class="keywordflow">if</span> self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aab73d1b44efb032b62ccf3ba1dd066b1">m_ltype</a> == <span class="stringliteral">&#39;continuos&#39;</span>:
<a name="l00225"></a>00225             (xgrid, ygrid) = meshgrid(self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>[1:-1], self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>[1:-1])
<a name="l00226"></a>00226             <span class="keywordflow">for</span> (i, val) <span class="keywordflow">in</span> izip(count(), c_[xgrid.flatten(), ygrid.flatten()]):
<a name="l00227"></a>00227                 load[i] = self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a4ec5b6d97eb06e7b6a84bd16be4c6c22">_eval_continuos_load</a>(val)
<a name="l00228"></a>00228         <span class="keywordflow">else</span>:
<a name="l00229"></a>00229             (xgrid, ygrid) = meshgrid(self.m_xgposi[1:-1], self.m_ygposi[1:-1])
<a name="l00230"></a>00230             <span class="keywordflow">for</span> (i, val) <span class="keywordflow">in</span> izip(count(), c_[xgrid.flatten(), ygrid.flatten()]):
<a name="l00231"></a>00231                 load[i] = self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a40e76e2182fb36721d46a0189cc793bf">_eval_discrete_load</a>(val)
<a name="l00232"></a>00232         <span class="keywordflow">return</span> load
<a name="l00233"></a>00233 
<a name="l00234"></a>00234     <span class="keyword">def </span>__assemble_rhs(self):
<a name="l00235"></a>00235         <span class="stringliteral">&quot;&quot;&quot; compute rhs vector. &quot;&quot;&quot;</span>
<a name="l00236"></a>00236 
<a name="l00237"></a>00237         (nxpts, nypts) = (self.m_nx_pts - 2, self.m_ny_pts - 2)
<a name="l00238"></a>00238 
<a name="l00239"></a>00239         <span class="comment"># Get Load</span>
<a name="l00240"></a>00240         rhs = self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a0293665f1db42b303ddebb00896aabba">__get_load</a>()
<a name="l00241"></a>00241 
<a name="l00242"></a>00242         <span class="comment"># Add boundary conditions</span>
<a name="l00243"></a>00243 
<a name="l00244"></a>00244         (dx2, dy2) = (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aeab92cfb5555af93f50f30ec33483881">m_dx</a> ** 2, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a017d63e67d5db1c3fe99db3e76d7c89a">m_dy</a> ** 2)
<a name="l00245"></a>00245         rhs[0:nxpts] += self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a13a04da3595fe00cd04c52009a098d17">m_vbott</a>[1:-1] / dy2
<a name="l00246"></a>00246         rhs[-nxpts:] += self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aad8f636d52615cd0fe663c7d5a8c8fc1">m_vtop</a>[1:-1] / dy2
<a name="l00247"></a>00247 
<a name="l00248"></a>00248         indx = nxpts * asarray(range(0, nypts), <span class="stringliteral">&#39;int&#39;</span>)
<a name="l00249"></a>00249         rhs[indx] += self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a2c48b2c09079e26101bb882e86250edd">m_vleft</a>[1:-1] / dx2
<a name="l00250"></a>00250         rhs[-(indx[::-1] + 1)] += self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a9b86acf66c46bfa5519828984fff2cd2">m_vright</a>[1:-1] / dx2
<a name="l00251"></a>00251 
<a name="l00252"></a>00252         <span class="keywordflow">return</span> rhs
<a name="l00253"></a>00253 
<a name="l00254"></a>00254     <span class="keyword">def </span>__assemble_matrix(self):
<a name="l00255"></a>00255         <span class="stringliteral">&quot;&quot;&quot; assemble matrix &quot;&quot;&quot;</span>
<a name="l00256"></a>00256 
<a name="l00257"></a>00257         rhs_len = self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a06aa951c5a8718334ceec867d234aaaf">m_load_len</a>
<a name="l00258"></a>00258         (dx2, dy2) = (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aeab92cfb5555af93f50f30ec33483881">m_dx</a> ** 2, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a017d63e67d5db1c3fe99db3e76d7c89a">m_dy</a> ** 2)
<a name="l00259"></a>00259         (nxpts, nypts) = (int(self.m_nx_pts - 2), int(self.m_ny_pts
<a name="l00260"></a>00260                       - 2))
<a name="l00261"></a>00261 
<a name="l00262"></a>00262         <span class="comment"># Main Diagonal</span>
<a name="l00263"></a>00263 
<a name="l00264"></a>00264         shape = (rhs_len, 1)
<a name="l00265"></a>00265         diag = 2. * ones(shape) * (1. / dx2 + 1. / dy2)
<a name="l00266"></a>00266 
<a name="l00267"></a>00267         <span class="comment"># Off Diagonals</span>
<a name="l00268"></a>00268 
<a name="l00269"></a>00269         pattx = ones(nxpts)
<a name="l00270"></a>00270         pattx[-1] = 0
<a name="l00271"></a>00271         diag_1 = -tile(pattx, nypts) / dx2  <span class="comment"># lower</span>
<a name="l00272"></a>00272         diag_nx = -ones(shape) / dy2  <span class="comment"># lower</span>
<a name="l00273"></a>00273         diag1 = roll(diag_1, 1)  <span class="comment"># upper</span>
<a name="l00274"></a>00274         diagnx = -ones(shape) / dy2  <span class="comment"># upper</span>
<a name="l00275"></a>00275 
<a name="l00276"></a>00276         <span class="comment"># Assemble</span>
<a name="l00277"></a>00277 
<a name="l00278"></a>00278         diags = [0, -1, -nxpts, 1, nxpts]
<a name="l00279"></a>00279         data = asarray([list(diag.flatten()), list(diag_1.flatten()),
<a name="l00280"></a>00280                        list(diag_nx.flatten()), list(diag1.flatten()),
<a name="l00281"></a>00281                        list(diagnx.flatten())])
<a name="l00282"></a>00282 
<a name="l00283"></a>00283         <span class="keywordflow">return</span> spdiags(data, diags, rhs_len, rhs_len).tocsc()
<a name="l00284"></a>00284 
<a name="l00285"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aae114553f4e217ff95716e0c06d11765">00285</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aae114553f4e217ff95716e0c06d11765">discretize</a>(self):
<a name="l00286"></a>00286         <span class="stringliteral">&quot;&quot;&quot; discretize pde &quot;&quot;&quot;</span>
<a name="l00287"></a>00287 
<a name="l00288"></a>00288         self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a032131b3687e8715b976800f754a88a0">set_up_engine</a>()
<a name="l00289"></a>00289         <span class="keywordflow">return</span> (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a833bde426b0fa9be68cedc7d0c5d4d98">__assemble_matrix</a>(), self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#af9845383c7f9458e788fe8fc12232a3c">__assemble_rhs</a>())
<a name="l00290"></a>00290 
<a name="l00291"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a2971e70feab948ffa2c573ce1fe6ac31">00291</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a2971e70feab948ffa2c573ce1fe6ac31">get_rhs</a>(self):
<a name="l00292"></a>00292         <span class="stringliteral">&quot;&quot;&quot; get right hand side &quot;&quot;&quot;</span>
<a name="l00293"></a>00293 
<a name="l00294"></a>00294         <span class="keywordflow">return</span> self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#af9845383c7f9458e788fe8fc12232a3c">__assemble_rhs</a>()
<a name="l00295"></a>00295 
<a name="l00296"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ad7c9f2390b43834f93c89e6284253e9b">00296</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ad7c9f2390b43834f93c89e6284253e9b">get_discretized_bc</a>(self):
<a name="l00297"></a>00297         <span class="stringliteral">&quot;&quot;&quot; returns dirichlet bc as vectors. &quot;&quot;&quot;</span>
<a name="l00298"></a>00298 
<a name="l00299"></a>00299         <span class="keywordflow">return</span> (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a13a04da3595fe00cd04c52009a098d17">m_vbott</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aad8f636d52615cd0fe663c7d5a8c8fc1">m_vtop</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a2c48b2c09079e26101bb882e86250edd">m_vleft</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a9b86acf66c46bfa5519828984fff2cd2">m_vright</a>)
<a name="l00300"></a>00300 
<a name="l00301"></a>00301 
<a name="l00302"></a>00302     @classmethod
<a name="l00303"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aba3d4b76d9c7f15f9f4193a67af6bd6e">00303</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aba3d4b76d9c7f15f9f4193a67af6bd6e">post_process</a>(cls, nx_opts, ny_opts, vbott, vtop, vleft, vright, vsol):
<a name="l00304"></a>00304         <span class="stringliteral">&quot;&quot;&quot; post process results &quot;&quot;&quot;</span>
<a name="l00305"></a>00305 
<a name="l00306"></a>00306         solu = empty((ny_opts, nx_opts))
<a name="l00307"></a>00307 
<a name="l00308"></a>00308         (solu[-1, :], solu[0, :]) = (vbott.flatten(), vtop.flatten())
<a name="l00309"></a>00309         (solu[:, 0], solu[:, -1]) = (vleft.flatten(), vright.flatten())
<a name="l00310"></a>00310 
<a name="l00311"></a>00311         (nxpts, nypts) = (int(nx_opts - 2), int(ny_opts - 2))
<a name="l00312"></a>00312         tmp = vsol.reshape((nypts, nxpts))
<a name="l00313"></a>00313         <span class="keywordflow">for</span> posi <span class="keywordflow">in</span> range(0, nypts):
<a name="l00314"></a>00314             solu[-(posi + 2), 1:-1] = tmp[posi, :]
<a name="l00315"></a>00315 
<a name="l00316"></a>00316         <span class="keywordflow">return</span> solu
<a name="l00317"></a>00317 
<a name="l00318"></a>00318 
<a name="l00319"></a><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a4ab69dead9d4d01010641193e3bb5699">00319</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a4ab69dead9d4d01010641193e3bb5699">solve</a>(self):
<a name="l00320"></a>00320         <span class="stringliteral">&quot;&quot;&quot; discretize and solve pde &quot;&quot;&quot;</span>
<a name="l00321"></a>00321 
<a name="l00322"></a>00322         (stiff_mat, rhs) = self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aae114553f4e217ff95716e0c06d11765">discretize</a>()
<a name="l00323"></a>00323 
<a name="l00324"></a>00324         tmp = spsolve(stiff_mat, rhs)
<a name="l00325"></a>00325         solu = self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aba3d4b76d9c7f15f9f4193a67af6bd6e">post_process</a>(self.m_nx_pts, self.m_ny_pts,
<a name="l00326"></a>00326                                 self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a13a04da3595fe00cd04c52009a098d17">m_vbott</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#aad8f636d52615cd0fe663c7d5a8c8fc1">m_vtop</a>,
<a name="l00327"></a>00327                                 self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a2c48b2c09079e26101bb882e86250edd">m_vleft</a>[::-1], self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a9b86acf66c46bfa5519828984fff2cd2">m_vright</a>[::-1],
<a name="l00328"></a>00328                                 tmp)
<a name="l00329"></a>00329 
<a name="l00330"></a>00330         <span class="keywordflow">return</span> (self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#ae4aeaee12ab324628b7afddb0b66fdfe">m_xgrid</a>, self.<a class="code" href="classmodels_1_1Poisson2DFiniteDifference_1_1Poisson2DFiniteDifference.html#a8df6dfb484d37a0bc6624f4fd2c6af09">m_ygrid</a>, solu)
<a name="l00331"></a>00331 
</pre></div></div>
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